The above described microchannel devices might be also well suited for creation of a sufficiently large gradient of an applied magnetic field to realize the coupling between the spin states and orbital states of SE. For example, stripes of a ferromagnetic material, such as Cobalt or Permalloy, can be easily fabricated by lithography and evaporation, and placed along the channels. Magnetization of the material in an applied uniform magnetic field would produce a nonuniform stray field outside the material, while the close proximity of the stripes to SE confined in the microchannels ensures that the field gradient experienced by the electrons is sufficiently large. For example, our finite-element modeling (FEM) calculations show that 200-nm thick stripes of Cobalt placed at the bottom of a 4-\(\mu \) m deep channel filled with the superfluid helium would produce a gradient on the order 10 Gauss/\(\mu \) m near the liquid surface. This would result in the difference between the Zeeman splittings for the ground state and the first excited Rydberg state of a surface-bound electron on the order of 1 MHz. This is comparable to the intrinsic linewidth of the corresponding Rydberg transition at temperatures below 1 K [1]}.
